I got herniated discs on my lower back and the military press has been aggrevating it. What can I replace it with.

Arnold press, strict press, landmine press.

Those would still put weight on my discs.

Seated dumbbell presses is about the only thing I can think of. Pushing your upper back into the bench should alleviate the pressure on the lower back.

lateral raises for days

This. I’d think any sort of pressing would put the most pressure on your back. Rear delt machine work could be good too

Cable lateral raise, idk if you got a hammer strenght shoulder machine at your gym.but its a good option too

does using a belt help with the pain?